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C₂×#9853 #206365

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,10,8,11,6,16)(5,12,15,17,13,18,14,9)(19,20)(21,27)(22,24)(23,31)(25,29)(26,30)(28,33)(32,34);(3,5)(4,9,11,17)(6,14)(7,15)(8,13)(10,12,16,18)(20,24)(21,28)(26,31)(29,34);(5,13)(9,17)(12,18)(14,15)(19,21,23,29,22,28,30,34)(20,25,26,27,24,32,31,33)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 113561);